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Lesson: Symmetric and Skew-Symmetric Matrices

Sample Question Videos

Worksheet • 16 Questions • 1 Video

Q1:

If is a symmetric matrix, what are the values of π‘₯ , 𝑦 , and 𝑧 ?

  • A π‘₯ = 9 , 𝑦 = 0 , 𝑧 = βˆ’ 5
  • B π‘₯ = βˆ’ 6 , 𝑦 = 0 , 𝑧 = βˆ’ 5
  • C π‘₯ = 9 , 𝑦 = 0 , 𝑧 = βˆ’ 1 7
  • D π‘₯ = 9 , 𝑦 = βˆ’ 1 2 , 𝑧 = βˆ’ 1 7
  • E π‘₯ = βˆ’ 9 , 𝑦 = 0 , 𝑧 = βˆ’ 5

Q2:

If is a symmetric matrix, what are the values of π‘₯ , 𝑦 , and 𝑧 ?

  • A π‘₯ = βˆ’ 2 , 𝑦 = 0 , 𝑧 = βˆ’ 1
  • B π‘₯ = βˆ’ 3 , 𝑦 = 0 , 𝑧 = βˆ’ 1
  • C π‘₯ = βˆ’ 2 , 𝑦 = 0 , 𝑧 = 9
  • D π‘₯ = βˆ’ 2 , 𝑦 = 1 0 , 𝑧 = 9
  • E π‘₯ = 6 , 𝑦 = 0 , 𝑧 = βˆ’ 1

Q3:

Which of the following matrices is skew-symmetric?

  • A  0 βˆ’ 3 βˆ’ 5 3 0 1 0 5 βˆ’ 1 0 0 
  • B  1 0 βˆ’ 9 βˆ’ 2 βˆ’ 9 βˆ’ 2 βˆ’ 5 βˆ’ 2 βˆ’ 5 4 
  • C  0 βˆ’ 1 βˆ’ 9 1 0 βˆ’ 6 9 6 7 
  • D  3 βˆ’ 5 βˆ’ 2 5 βˆ’ 3 1 2 βˆ’ 1 3 

Q4:

Which of the following matrices is skew-symmetric?

  • A  0 βˆ’ 3 4 3 0 8 βˆ’ 4 βˆ’ 8 0 
  • B  βˆ’ 9 βˆ’ 6 7 βˆ’ 6 2 βˆ’ 3 7 βˆ’ 3 βˆ’ 3 
  • C  0 βˆ’ 4 4 4 0 6 βˆ’ 4 βˆ’ 6 9 
  • D  3 1 8 βˆ’ 1 βˆ’ 1 1 βˆ’ 8 βˆ’ 1 4 

Q5:

Which of the following matrices is skew-symmetric?

  • A  0 4 βˆ’ 9 βˆ’ 4 0 3 9 βˆ’ 3 0 
  • B  2 8 βˆ’ 3 8 3 5 βˆ’ 3 5 βˆ’ 8 
  • C  0 1 0 7 βˆ’ 1 0 0 8 βˆ’ 7 βˆ’ 8 6 
  • D  2 2 βˆ’ 8 βˆ’ 2 7 βˆ’ 1 0 8 1 0 βˆ’ 1 0 

Q6:

If 𝐴 and 𝐡 are symmetric matrices, does it follow that 𝐴 𝐡 is also symmetric?

  • Ayes
  • Bno

Q7:

Given that the matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q8:

Given that the matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q9:

Given that the matrix is skew-symmetric, find the value of π‘₯ + 𝑦 + 𝑧 .

Q10:

Suppose that 𝐴 and 𝐡 are symmetric matrices and that 𝐴 𝐡 = 𝐡 𝐴 . Does it follow that 𝐴 𝐡 is also a symmetric matrix?

  • Ano
  • Byes

Q11:

Find the value of π‘₯ which makes the following a symmetric matrix.

Q12:

Find the value of π‘₯ which makes the following a symmetric matrix.

Q13:

Find the value of π‘₯ which makes the following a symmetric matrix.

Q14:

The non-zero eigenvalues of a real, skew-symmetric matrix are .

  • Anon-negative
  • Bpurely imaginary
  • Cpurely real

Q15:

Which of the following matrices is symmetric?

  • A  βˆ’ 2 3 5 3 βˆ’ 4 βˆ’ 3 5 βˆ’ 3 βˆ’ 7 
  • B  βˆ’ 4 βˆ’ 4 2 βˆ’ 4 8 βˆ’ 2 8 βˆ’ 2 3 
  • C  βˆ’ 2 4 βˆ’ 3 4 βˆ’ 8 βˆ’ 8 9 βˆ’ 3 βˆ’ 2 
  • D  βˆ’ 3 βˆ’ 5 βˆ’ 1 βˆ’ 6 6 5 βˆ’ 7 7 βˆ’ 8 

Q16:

Which of the following matrices is symmetric?

  • A  5 βˆ’ 7 βˆ’ 2 βˆ’ 7 βˆ’ 1 0 9 βˆ’ 2 9 βˆ’ 7 
  • B  βˆ’ 6 βˆ’ 6 1 0 βˆ’ 6 4 βˆ’ 1 9 6 βˆ’ 4 
  • C  βˆ’ 4 βˆ’ 7 βˆ’ 3 βˆ’ 4 9 βˆ’ 6 βˆ’ 6 4 βˆ’ 1 
  • D  βˆ’ 5 1 0 βˆ’ 7 βˆ’ 8 3 3 βˆ’ 8 1 8 
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